Question: A circle with circumference ${10}$ has an arc with a $162^\circ$ central angle. What is the length of the arc?
The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{162}^\circ}{360^\circ} = \dfrac{{s}}{{{10}}}$ $\dfrac{9}{20} = \dfrac{{s}}{{10}}$ $\dfrac{9}{20} \times {10} = {s}$ $\dfrac{9}{2} = {s}$ ${10}$ ${162^\circ}$ ${\dfrac{9}{2}}$